In this direction, Mordant and Segers [1]} showed that in Gaussian case \(\mathcal {P} = \mathcal {N}(0, 1)\)  it is true that
\({\mathbb {E}}{\max \limits _{\pi \in \mathcal {S}_n} S(\pi )} = n \sqrt{2 \log {n}} (1 + o(1)),\) 
